What is 10/13 plus 11/13? (Answer: 21/13)

Exact Answer

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Problem: What is 10/13 plus 11/13?
Formula / Expression: 10/13 + 11/13
Final Answer: 1 8/13 (21/13)
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Step-by-Step Solution:

Step 1: Check the Denominators (Like Fractions)
Both fractions already share the identical denominator (13). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 13.
Working: 10/13 + 11/13

Step 2: Add the Numerators
Now add the numerators (10 + 11 = 21) and keep the common denominator 13 unchanged.
Working: 10 + 11/13 = 21/13

Step 3: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 21 and 13 is 1, confirming that 21/13 cannot be reduced further—it is already in its simplest irreducible form.
Working: 21/13

Step 4: Convert Improper Fraction to a Mixed Number
Since the numerator (21) is greater than the denominator (13), divide 21 by 13: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/13.
Working: 21/13 = 1 8/13

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 13 produces a repeating decimal (approximately 1.615385, or 161.5385%).
Working: 21 ÷ 13 = 1.615385 (161.5385%)

Key Values:
- Simplified Fraction: 21/13
- Mixed Number Form: 1 8/13
- Decimal Value: 1.615385
- Percentage: 161.5385%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-13-plus-11-13/
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10/13 + 11/13 = 21/13

Simplified Fraction

21/13

Mixed Number

1 8/13

Decimal Value

1.615385

Percentage

161.5385%

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Step-by-Step Solution: 10/13 + 11/13

Step 1

Check the Denominators (Like Fractions)

Both fractions already share the identical denominator (13). Because these are like fractions, no conversion to a common denominator is required—we directly add their numerators while keeping the denominator 13.

10/13 + 11/13

Step 2

Add the Numerators

Now add the numerators (10 + 11 = 21) and keep the common denominator 13 unchanged.

10 + 11/13 = 21/13

Step 3

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 21 and 13 is 1, confirming that 21/13 cannot be reduced further—it is already in its simplest irreducible form.

21/13

Step 4

Convert Improper Fraction to a Mixed Number

Since the numerator (21) is greater than the denominator (13), divide 21 by 13: it goes in 1 whole time(s) with a remainder of 8, giving the mixed number 1 8/13.

21/13 = 18/13

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 13 produces a repeating decimal (approximately 1.615385, or 161.5385%).

21 ÷ 13 = 1.615385 (161.5385%)

Visual Representation

The diagram below illustrates 10/13 plus 11/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/13`
Mixed Number Form	`1 8/13`
Decimal Form	`1.615385`
Percentage	`161.5385%`

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Frequently Asked Questions

What is 10/13 plus 11/13 as a fraction?

10/13 + 11/13 in simplest fraction form is 21/13 (or 1 8/13 as a mixed number).

What is 10/13 plus 11/13 as a decimal?

10/13 + 11/13 converted to a decimal is 1.615385.

What is 10/13 plus 11/13 as a percentage?

10/13 + 11/13 expressed as a percentage is 161.5385%.

How do you write 10/13 plus 11/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 21/13 can be written as the mixed number 1 8/13.

Does 10/13 plus 11/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.615385...) because the denominator contains prime factors other than 2 and 5.